A1529
Title: Pairwise maximum likelihood for multi-class logistic regression model with multiple rare classes
Authors: Xuetong Li - Xian Jiaotong University (China)
Danyang Huang - Renmin University of China (China)
Xuetong Li - Central University of Finance and Economics (China) [presenting]
Abstract: The problem of multi-class logistic regression with one major class and multiple rare classes is studied, which is motivated by a real application in TikTok live stream data. The model is inspired by the two-class logistic regression model but with surprising theoretical findings, which in turn motivate new estimation methods with excellent statistical and computational efficiency. Specifically, since rigorous theoretical analysis suggests that the resulting maximum likelihood estimators of different rare classes should be asymptotically independent, multiple pairwise two-class logistic regression problems are considered instead of optimizing the joint log-likelihood function with computational challenge in multi-class problem, which are computationally much easier and can be conducted in a fully parallel way. To further reduce the computation cost, a subsample-based pairwise likelihood estimator is developed by downsampling the major class. It is shown rigorously that the resulting estimators could be as asymptotically efficient as the global maximum likelihood estimator under appropriate regularity conditions. Extensive simulation studies are presented to support the theoretical findings and a TikTok live stream dataset is analyzed for illustration purpose.
